(untitled) (Contemporary Mathematics, 2023)
There is no single set in an imaginary space, for which an exact mathematical definition would not exist by the mathematical symmetry laws. We discuss a theory in which appears an imaginary number axis strictly defifined at the level of imaginary space, allowing one to formulate and prove the theorem on the basis of its internal disclosure. This new theory of a set makes it possible to introduce a notion of the full compactness of sets of an imaginary space, confirming their availability in the defined symmetry of elements of a definitely symmetrical line.